I don’t disagree, but that has nothing to do with the UKs constitutional set up. That is the reality EVERYWHERE. We try to build societies where IN THEORY everyone has the same chances. But in reality that’s just not true. In theory every UK citizen (do you have to have a certain age or have a party affiliation?) can become PM. In reality this career path is not open to everyone.That is factually incorrect
I get the argument to say, that if you look just on paper, an unelected HoS should be made into an elected role. There are many good theoretical arguments for it. In reality though it doesn’t make much of a difference for the society. In the end, what we might deem an equal, successful society depends much more on other things than such principles.
I can appreciate that for other the theoretical background is important to tackle first. In my POV that’s not always the case. The UK could solve many of its problems and issues under a monarch just fine. It’s a bit of a hen/egg problem and depending what side you sit on, you definitely dismiss the need for such a change or you think it’s absolutely necessary and a first step.